Ask question

Ask question

All categories

3 years ago

9

A newspaper ad includes a telephone number 1-555-dial vsw. How many seven letter arrangements are possible for the phone number

using the 26 letters of the alphabet of no letter is ised more than once? Express your answer using scientific notation.

1 answer:

trapecia [35]3 years ago

7 0

Let u be the set of all words containing 7 letters(26 letters to the power 7)

You might be interested in

james' daily wage was $5 more than Davis's. Although James worked 3 days less than David, they earned $180 each. Find the number

zalisa [80]

Answer: 9 days

Step-by-step explanation:

Let x represent James' daily wage

James' daily wage was $5 more than Davis's. It means that Davis's daily wage will be $(x-5)

Let y represent number of days that James worked. James worked 3 days less than David. It means that the number of days that Davis worked would be (y + 3) days

they earned $180 each. Total amount of money earned by either of of them is the product of wage and the number of days worked.

Since James earned $180, then

180 = xy - - - - - - - - 1

Since Davis also earned $180, then

180 = (x - 5)(y + 3)

xy +3x -5y -15 = 180 - - - - - - - - 2

Substituting xy = 180 into equation 2

It becomes

180 + 3x - 5y -15 = 180

3x - 5y = 180 - 180 + 15

3x - 5y = 15 - - - - - - -3

From equation 1, x = 180/y

Substituting x = 180/y into equation 3, it becomes

3 × 180/y - 5y = 15

540 - 5y^2 = 15y

5y^2 + 15y -540 = 0

Dividing through by 5

y^2 + 3y -108 = 0

y^2 + 12y - 9y -108 = 0

y(y + 12) - 9(y + 12) = 0

y + 12 = 0 or y - 9 = 0

y = -12 or y = 9

Since the number of days cannot be negative, then,

Number of days that James worked will be 9 days

8 0

3 years ago

When obtaining a confidence interval for a population mean in the case of a finite population of size N and a sample size n whic

Elanso [62]

Answer:

95% Confidence interval for the mean

$142.8 \leq\mu\leq158.4$

Step-by-step explanation:

We have to calculate a 95% confidence interval for the mean of a finite population.

The error is multiplied by the following finite population correction factor:

$cf=\sqrt{\frac{N-n}{N-1} }$

The standard deviation can be estimated as

$\sigma=\frac{s}{\sqrt{n}} \sqrt{\frac{N-n}{N-1} } =\frac{24.4}{\sqrt{32} }* \sqrt{\frac{200-32}{200-1} }=3.963$

The 95% confidence interval has a z value of 1.96, so it becomes:

$M-z*\sigma_c\leq\mu\leq M+z*\sigma_c\\\\150.6-1.96*3.963\leq\mu\leq 150.6+1.96*3.963\\\\ 142.8 \leq\mu\leq 158.4$

5 0

3 years ago

a) The quadratic 3x^2-12x-11 can be written in the form 3(x+a)^2+b. Find the values of a and b. b) Given that the solutions of t

LenKa [72]

Answer:

Step-by-step explanation:

a) 3x^2-12x-11=3*x^2-3*2*2*x+3*4-23=3*(x^2-2*2x+2^2)-23=3*(x-2)^2-23

so a= -2 ,b= -23

b) x1=[12+V(12^2-4*3* -11)]/6=12/6+V(144+132)/6=2+2/6V69=2+1/3V69=

2+V69/9=2+V23/3

c=2, d= 23/3

5 0

3 years ago

The Caesar Cipher of the sentence "THIS MESSAGE IS TOP SECRET."

vagabundo [1.1K]

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

"THIS MESSAGE IS TOP SECRET."

We need to use the Caesar cipher.

As in general we always take a shift of 3 keys in Caesar cipher.

so, According to shift of 3 keys it becomes,

T→W

H→K

I→L

S→V

M→P

E→H

A→D

G→J

O→R

C→F

R→U

P→S

So, it can be written as

"THIS MESSAGE IS TOP SECRET."

WKLVP HVVDJ HLVWR SVHFU HW.

we make a set of 5 letters in a word after Caesar cypher.

Hence, Option 'a' is correct.

8 0

3 years ago

Scientific notation<br> 9.78 × 10^5 - 732,000<br> It has to be either 2.46 × 10^5 or 2.46 × 10^3

Morgarella [4.7K]

Answer:

$2.46\times 10^5$

Step-by-step explanation:

$9.78 \times 10^5 - 732,000\\= 9.78 \times 10^5 - 7.32 000\times 10^5\\= 9.78 \times 10^5 - 7.32\times 10^5\\= 2.46\times 10^5$

3 0

3 years ago